That's a feature of the iPhone operating system called iCloud, which automatically syncs the stuff on your phone for backup purposes in case you need to restore. This is what iCloud backs up:
-Photos and videos in the Camera Roll
-Device settings (for example: Phone Favorites, Wallpaper, and Mail, Contacts, ---Calendar accounts)
-Home screen and app organization
-Messages (iMessage, SMS, and MMS)
You're automatically asked if you want to restore data using iCloud when you purchase a new device, however I think Verizon should have let know you of this feature. I hope my answer was helpful.
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I have been in the cellular phone industry for 12 years, I have worked the front lines as far as sales and tech support. I am knowlegable in many aspects of the industry.
ImVerizon does not do this for you. However, if you have used your computer to backup your IPhone through ITunes, then you can restore your texts. Apple can walk you through this. Verizon stores do not save customers' personal data onto their computers .. I hope this clears up any misunderstanding!
Solving problems one phone at a time! Over a decade of wireless experience with 4 years at VZW... I can answer it all!